#### opus

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There are 3 criterias that need to be met:

1) a*b is defined for every ordered pair (a,b) of elements of A.

2) a*b must be uniquely defined (unambiguous).

3) If a and b are in A, a*b must be in A.

Trying to figure out if subtraction meets these criterias on the integers. I know that we define subtraction in terms of addition, but I'm trying to go at this from scratch.

Now I have a couple questions that I'm unsure of.

For criteria 1: a*b needs to be defined for every (a,b) in A. But defined in terms of what? Axioms? If so, what axioms?

For criteria 2: Im not sure how to determine if this is uniquely defined. I know that a-b is unambiguous, in the sense of our daily use of it. But I'm not sure if I should be thinking about it that way.